# Permutations and Combinations Quiz Set 004

### Question 1

How many four letter words, with all the letters different, can be formed out of the letters of the word 'BACKGROUND'?

A

5040.

B

5050.

C

5030.

D

5060.

Soln.
Ans: a

This word has 10 different letters. The number of possibilities is 10P4 = 5040.

### Question 2

What is the value of 5P3?

A

60.

B

70.

C

50.

D

80.

Soln.
Ans: a

5P3 is \${5 !}/{(5 - 3) !}\$ = 60.

### Question 3

6 men are standing in front of 7 cabins. In how many ways can they enter the cabins?

A

5040.

B

5045.

C

5038.

D

5041.

Soln.
Ans: a

The first has 7 options, the second has (7 - 1), and so on. This is expressed as 7P6, which evaluates to 5040.

### Question 4

There are 3 trains between two stations A and B. In how many ways can a student go from A to B and return by a different train?

A

6.

B

11.

C

4.

D

7.

Soln.
Ans: a

The upward journey is possible in 3 ways, and the downward in 2 ways. So the outcomes are 3 × 2 = 6.

### Question 5

In how many ways can 2 letter words be formed by using a given set of 13 consonants?

A

156.

B

161.

C

154.

D

157.

Soln.
Ans: a

The first place can get any of the 13 consonants, the second place can then get (13 - 1), and likewise. This is expressed as 13 × 12, which evaluates to 156. 